Yes, adding ‘chemicals’ is certainly not the way to go. I do not see many or any being able to manage high nutrients naturally though. Still, the lanthanum chloride route seems to be a feasible way to manager high phosphsates without stressing corals or reducing trace elements significantly from growing algae in a scrubber or refugium - btw, why do you think you can grow algae in a reactor when you were not able to grow them in a refugium? This is typically an issue with insufficient traces if light and nutrients are ruled out.
The way to manage high nutrients in my opinion is limited to a) regular water changes, b) feeding appropriate to the tank size, c) keeping enough (large) corals to absorb them, d) right size the skimmer (do you have the 220 or smaller/bigger), and balancing dry and frozen food depending on if nitrate or phosphate are higher. The only other thing I do is carbon dosing by using Elimi NP from Tropic Marin (not vodka etc).